We report spectral, imaging, and variability results from four new XMM-Newton observations and two new Chandra observations of high-redshift (z > 4) radio-loud quasars (RLQs). Our targets span lower, and more representative, values of radio loudness than those of past samples of high-redshift RLQs studied in the X-ray regime. Our spectral analyses show power-law X-ray continua with a mean photon index, Gamma =1.74 +/- 0.11, that is consistent with measurements of lower redshift RLQs. These continua are likely dominated by jet-linked X-ray emission, and they follow the expected anti-correlation between photon index and radio loudness. We find no evidence of iron Kalpha ~ emission lines or Compton-reflection continua. Our data also constrain intrinsic X-ray absorption in these RLQs. We find evidence for significant absorption (N_H ~ 10^22 cm^-2) in one RLQ of our sample (SDSS J0011+1446); the incidence of X-ray absorption in our sample appears plausibly consistent with that for high-redshift RLQs that have higher values of radio loudness. In the Chandra observation of PMN J221-2719 we detect apparent extended (~ 14 kpc) X-ray emission that is most likely due to a jet; the X-ray luminosity of this putative jet is ~2% that of the core. The analysis of a 4.9 GHz VLA image of PMN J221-2719 reveals a structure that matches the X-ray extension found in this source. We also find evidence for long-term (450-460 days) X-ray variability by 80-100% in two of our targets.